Mie Scattering

Mie Scattering is a method for simulating the scattering of electromagnetic waves (light) by spheres. Based on the robust FORTRAN implementation by Warren Wiscombe, this software offers researchers and scientists an accurate and reliable tool for Mie scattering calculations.

Features

Accurate simulation of scattering for small to very large sphere sizes (𝜋d/λ > 10,000)
Tested against MIEV0 <https://www.researchgate.net/publication/253485579_Mie_Scattering_Calculations_Advances_in_Technique_and_Fast_Vector-speed_Computer_Codes>_ implementation
Used to a web-based Mie calculator <https://omlc.org/calc/mie_calc.html>_

The source code is written in CWEB <https://github.com/ascherer/cweb>_, which allows excellent documentation of scientific programs. Basically, there is a program ctangle that converts cweb code to C. There is another program cweave that converts cweb code to TeX. This then generates nicely documented source code <https://github.com/scottprahl/mie/blob/main/doc/mie_doc.pdf>_.

Getting Started

Downloading


Clone the repository using git or download the source code as a zip file:

.. code-block:: shell

    git clone https://github.com/scottprahl/mie.git

Installation

Unix/macOS ^^^^^^^^^^

Run the following command to build and install:

.. code-block:: shell

make install

The executable will be installed as /usr/local/bin/mie.

Windows ^^^^^^^

Download the latest executable from the Releases page <https://github.com/scottprahl/mie/releases>_.

Python Package ^^^^^^^^^^^^^^

I have written a pure python version of Mie scattering based on this code. miepython <https://github.com/scottprahl/miepython/> is a bit slower, but it allows one to run simulations in jupyterlab <https://jupyter.org> interactively.
Installation is easy:

.. code-block:: shell

pip install miepython

Usage

Here is a simple implementation that calculates scattering parameters from 360 nm latex spheres by UV-A light.

.. code-block:: c

#include <stdio.h>
#include <math.h>
#include "mie.h"

int main() {
    const double n_sphere = 1.59;
    const double n_medium = 1.34;
    const double diameter_nm = 360;
    const double sphere_density = 1.05; // gm/ml
    const double medium_density = 1.00; // gm/ml
    const double concentration = 0.01; // gm spheres/gm medium
    double x, qsca, g, sphere_area_cm2, sphere_volume_ml, number_per_cc, lambda_nm;

    printf("Sphere concentration is          %5.2g%% gm spheres/gm\n", concentration * 100);
    printf("Medium refractive index is       %7.4f\n", n_medium);
    printf("Sphere refractive index is       %7.4f\n", n_sphere);
    printf("The density of the spheres is    %7g gm/ml\n", sphere_density);
    printf("The density of the medium is     %7g gm/ml\n", medium_density);
    printf("\n");
    printf("    d    lambda     x      N       Q_sca    g      mu_s    mu_s'\n");
    printf("  [nm]    [nm]     [-]   [#/ml]     [-]    [-]    [1/cm]  [1/cm]\n");

    for (lambda_nm = 315; lambda_nm <= 400; lambda_nm += 5) {
        x = (diameter_nm * M_PI) / (lambda_nm / (n_sphere / n_medium));
        sphere_area_cm2 = M_PI * pow(diameter_nm / 1e7, 2) / 4.0;
        sphere_volume_ml = M_PI * pow(diameter_nm / 1e7, 3) / 6.0;
        number_per_cc = 1 / (sphere_volume_ml * (1 + sphere_density / (medium_density * concentration)));
        ez_Mie(x, n_sphere / n_medium, &qsca, &g);

        printf("%7.1f %7.1f ", diameter_nm, lambda_nm);
        printf("%7.2f %7.2e %7.4f %7.5f ", x, number_per_cc, qsca, g);
        printf("%7.2f ", qsca * sphere_area_cm2 * number_per_cc);
        printf("%7.2f \n", (1 - g) * qsca * sphere_area_cm2 * number_per_cc);
    }
    return 0;
}

When compiled (see src/Makefile for details), this produces::

Sphere concentration is              1% gm spheres/gm
Medium refractive index is        1.3400
Sphere refractive index is        1.5900
The density of the spheres is       1.05 gm/ml
The density of the medium is           1 gm/ml

    d    lambda     x      N       Q_sca    g      mu_s    mu_s'
  [nm]    [nm]     [-]   [#/ml]     [-]    [-]    [1/cm]  [1/cm]
  360.0   315.0    4.26 3.86e+11  1.1711 0.86861  460.32   60.48 
  360.0   320.0    4.19 3.86e+11  1.1360 0.86600  446.54   59.84 
  360.0   325.0    4.13 3.86e+11  1.1024 0.86347  433.34   59.16 
  360.0   330.0    4.07 3.86e+11  1.0703 0.86102  420.70   58.47 
  360.0   335.0    4.01 3.86e+11  1.0395 0.85866  408.62   57.75 
  360.0   340.0    3.95 3.86e+11  1.0101 0.85640  397.04   57.02 
  360.0   345.0    3.89 3.86e+11  0.9818 0.85422  385.92   56.26 
  360.0   350.0    3.83 3.86e+11  0.9546 0.85212  375.22   55.49 
  360.0   355.0    3.78 3.86e+11  0.9282 0.85006  364.87   54.71 
  360.0   360.0    3.73 3.86e+11  0.9027 0.84803  354.83   53.93 
  360.0   365.0    3.68 3.86e+11  0.8779 0.84597  345.08   53.15 
  360.0   370.0    3.63 3.86e+11  0.8537 0.84384  335.59   52.41 
  360.0   375.0    3.58 3.86e+11  0.8302 0.84159  326.35   51.70 
  360.0   380.0    3.53 3.86e+11  0.8074 0.83919  317.36   51.04 
  360.0   385.0    3.49 3.86e+11  0.7851 0.83658  308.62   50.43 
  360.0   390.0    3.44 3.86e+11  0.7635 0.83375  300.13   49.90 
  360.0   395.0    3.40 3.86e+11  0.7426 0.83065  291.91   49.43 
  360.0   400.0    3.35 3.86e+11  0.7224 0.82729  283.98   49.05

License

This project is licensed under the BSD 3-clause License <https://github.com/scottprahl/mie/blob/main/LICENSE>_.

Citation

If you use this software in your research, please cite it as below:

.. code-block:: bibtex

@misc{prahl_mie,
  author = {Scott Prahl},
  title = {Mie Scattering},
  version = {v2.6.3},
  year = {2023},
  doi = {10.5281/zenodo.10087653},
  url = {https://github.com/scottprahl/mie}
}

scottprahl / mie

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